"The mighty fugue!" cries Chris Thile, devilishly dexterous and eclectic American mandolin player, as he polishes off the second movement of Bach's G minor Sonata for solo violin. The 32-year-old has been performing since he could hold up an instrument, and it shows – not just in his flash mandolin licks, but in his deftly lovable stage patter. He is funny, a bit wacky, and he held this crowd rapt for two hours.

Thile grew up playing bluegrass in bands such as Nickel Creek and Punch Brothers. His own meandering songs are born of that tradition but also flit from dirty blues to angular free improv to cute, self-deprecating numbers about hapless love affairs that he delivers with doe-eyed impishness and an unfaltering, soft-grained lilt. He laced numbers by Fiona Apple and the Louvin Brothers with breezy virtuosity that (mostly) kept to the better side of playful showing off.

But Thile's recent preoccupation is Bach, and this he does with no frills or fancy work. His latest album is solo music for violin, which, as it shares the same tuning as a mandolin, he can play note for note. His visual delivery takes some getting used to: he ducked and dived to the contours of the counterpoint, almost miming the musical drama and blissing out to the spiciest harmonies. It induced some initial sniggers from the audience, but comedy Bach this was not. Close your eyes and Thile's phrasing made real sense. His articulation was impeccable, his sense of line deeply felt. The dance movements moved like real dances, but he never sacrificed precision for swing. "The B minor Partita, like everything Bach wrote, is completely rad," he declared by way of introduction, and sure enough it induced the crowd's heartiest whoops of the night.

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